108 Dr. L. Silberstein on Molecular 



observable E=/ul 2 , that is, writing again ei 2 /m l = B 1 and 

 e 2 2 lm 2 = B 2 , 



(yi-7)^i--gr^2=iB 1 (K + 2)E a , 



2B 

 -- S r^i+(7a-7)^s=4B a (K + 2)E a , I 



(7i-7)«tfi=iBi(K + 2)E. ; (7.-7)W»=4B,(K + 2)E f , 



where # l9 y x and # 2 > 2/2 are the components of r x and r 2 along 

 and perpendicular to the individual molecular axis i, in the 

 plane E, i, and E a , E s the components of the external electric 

 vector E along and perpendicularly to the axis. Let that 

 molecular axis make with the (fixed) direction o£ E the 

 angle 0. Then E a =E cos 0, E S = E sin 0, and 



B l (K + 2) 

 e 1 x 1 = 



3D 



(72-7+ ^f)e cos 0; 



«iyi= -o7^ r E sin (9, 



m 3( 7l -7) 



with similar expressions for e 2 x 2 , e 2 y 2 . The vector e{t x + e 2 x 2 , 

 to be substituted in (10), falls into the direction of E, and its 

 tensor is £1(^1 cos 0+y\ sin 0) -f e 2 {x 2 cos 0+y 2 sin 0). Thus 

 we have, by (10), 



{B 1 (72-7) + B 2 ( 7l -7)+ 4 5r 2 }cos 2 ^ 



L7i — 7 72 — 7J 



that is, comparing with our former expressions for co s , co a , 



co = co s sin 2 + co a cos 2 0. 



The latter result could also be obtained at once by con- 

 sidering a) = gd s -f &) a i . i as the operation to which E is 

 subjected. 



Now, the average of cos 2 is 1/3 and that of sin 2 # is 

 2/3, so that we have, ultimately, for an isotropic diatomic 

 substance, 



ft> = o &>s + 3 &>«> (23) 



